@@ -37,29 +37,35 @@ The third assurance is correctness under a large number of rejections. The stand
3737| ML-DSA-44 | CA5A01E1 EA6552CB 5C980346 2B94C2F1 DC9D13BB 17A6ACE5 10D15705 6A2C6114 | A4652DC4 A2710952 68DD84A5 B0744DFD BE2E642E 4D41FBC4 329C2FBA 534C0E13 | 8C8CACA8 8FFF52B9 33051053 7B3701B3 993F3726 136A650F 48F86045 51550832 | B4B14220 9137397D AD504CAE D01D390A DAF49973 D8D2414F C3457FB7 AF775189
3838| ML-DSA-44 | 9C005F15 50B4F318 55C6B92F 97873673 3F37791C B39DD182 D7BA5732 BDC2483E | 2485AA99 345F1B33 4D4D94B6 10FBFFCC B626CBFD 4E9FF0E1 F6FC3509 3C423544 | B744343F 30F7FEE0 88998BA5 74E799F1 BF3939C0 6C29BF9A C10F3588 A57E21E2 | 5B80A60B AA480B9D 0C7D2C05 B50928C4 BF6808DD A6936420 58A3EB77 EAA768FC
3939| ML-DSA-44 | 4FAB5485 B009399E 8AE6FC3D 3EEFBFE8 E09796E4 477AABD5 EB1CC908 FA734DE3 | CB56909A 7CF3008A 662DC635 EDCB79DC 151CA7AC BAE17B54 4384ABD9 1BBBC1E9 | 7CAB0FDC F4BEA5F0 39137478 AA45C9C4 8EF96D90 6FC49F6E 2F138111 BF1B4A4E | 6CC38D73 D639682A BC556DC6 DCF436DE 24033091 F34004F4 10FABC68 87F77AB0
40- | ML-DSA-65 | CCD61917 2D0978FD B584D433 CB5A044C 8D24592D AD4D1E57 ECF1FD62 C40A309B | 756C734D B013F83E 295F2878 B32F1633 5D576249 B16D83AF EDE1F5D4 CC36D24F | 8A32D4B5 D3C8537A A9C7C952 F63959C6 6162A68D 5F3D02E6 C5F96E2C EA41D2EF | 958287F1 646D855B B065895A 6C6DA3DF 6A3F7AB2 A430C9DC 559D313E 7DD0A527
41- | ML-DSA-65 | C6315FC7 19895D16 454B7D62 084F0C8A 2903D8D0 0DC1D82E B3F45F06 463C6FBD | CEE1A1C7 F966A411 BB94C38A 0E33E1F7 102D3130 FA9C5D27 96F3F7F8 6ECF4B1D | D8CB8B23 931495FD F71477DB 7C335A15 1C6A9096 97F1C39A 3175133B 68881F28 | BD57A932 31EFEF6B 4E7FE374 E2194DB7 E00202EA F5EFC60D F5F9FE1C 5F579D06
42- | ML-DSA-65 | F005E473 8B528F95 3669A2BC A3925266 DBD23909 CD2C4DCE 50B980D7 89EBD0D4 | D3E33502 CCC035C9 B9195A27 14FE7ECE DD13DFF4 B854F237 6D993D38 A8E8AFF2 | EF1FE025 F8DF1FDC FDAFD188 F68B9D10 85AE8D09 234EBDAD 67DE985B A7347DE4 | 9E7B668C 51B250B1 2ED76665 BB4315CE 4BDBAF00 BF927F6D 895F0601 0D3BBC0E
43- | ML-DSA-65 | F215BA22 80D86F14 2012FC05 FFC04F2C 7D22FF5D D7D69AA0 EFB081E3 A53E9318 | 17FBD1D1 7DAACEA7 A2F6DA1F 22835E86 30E8AE8E F1A66E8B 7935CC6C C762532D | A4FADC3C 232F2ABC 8FCBB9C1 11F261E0 3DC2FF2D 57280A42 42936A63 E481AFE6 | C027D21B 21FA75AB E7F35CD8 4A54E2E8 3BD35214 0BC8C49E AB2C4500 4E7268A7
44- | ML-DSA-65 | A8E6C084 B3AAE469 0724631C AA57C10D F5973F95 38D25493 E264A4E2 B2C5A4E9 | D8B7DE2D A326EBAE 241D657E C090F4CA 3438DFFE ECE1BD05 D9CE7DFC 5204C6DC | A45A91B6 B2B392B7 087152D2 3E57E39A A78A42AB 91AAD034 4FB80393 F22FB0AE | C9DB2B64 2F739B32 ED5B14B8 FEEE6C77 9BAE7297 17D4FF11 CA281954 D8FF1B1D
45- | ML-DSA-87 | 5AC68A41 71730B1E 920CC3E7 CC4ACA79 C25A3621 0057373B 6BCEBCDF A144CE18 | 2446AB05 EEC3977C 40650338 983EEBF7 8942AC31 F5E94454 3E87DBAC 0A4889C1 | 172F6D49 AF757918 823A75E9 81D605DD AF74BF21 009AC836 D8B4C0AA BB49C14C | 3784755A C5A2D572 0623E504 707C3088 61EF4177 A6460FBE B4DB257A AA245B55
46- | ML-DSA-87 | E45F9CC0 43C2C0F4 BEBCAD28 60CADF77 C8211237 D7AAA108 A56E3ACA 92D207F7 | F5B727CA 02B6F302 5135926A 5FCA2A64 A800579C BFD44863 A08ABA5F E6C33B46 | 86B5A936 1F73427E BA3EEF5D 46112B74 67CEDFBC C77EF36C 94EF0666 C1AD37B6 | E8276BF4 D57752D7 7C6EAE2B 80050ED2 0CF15344 B69E5150 F9479290 3EA3790A
47- | ML-DSA-87 | 5E37A143 C0FFAEF6 00F33C37 6589069A 7A0CE2FA C36DBEFE C42C5A60 167D5A12 | C210312C 242E0642 F990328A BFCD1189 D24EB8E9 C122BB6D FEFCF02D 4FCF6224 | 9A72DFEB 5CDAD43D 3A416F8A D7B6676D 5528DDDA 661C3513 B6A460DB 74331F51 | B39E8111 5160026D A5528C40 B90EA146 64BFC22E 261023A7 DC419451 288ED93F
48- | ML-DSA-87 | 51DF520B 9084E48B 72EAEBA7 FE36B540 05CD963B 58CC25DE 79339948 FD561065 | 3ECF7F6A 89387291 18CC21A1 5B2B5933 7B24FD34 38FB132D 0162E53C 28CB374C | 28EFCAD1 C1B528E0 E46CB25D 28FA21DB A893010B 3C741D73 1460988B 66985D78 | 02FA4CF7 BF7F5BD1 3874C77B 30DAF708 BAA3E2C0 97D4298B F242A07B F68D7AD6
49- | ML-DSA-87 | 6857AF5C 878EFF78 92F1722D 8CE11F47 84B9D144 B50B23B5 3070963B 501054E6 | 9A2B47D3 4624BA79 7ECE8C7C 67FAADB2 B2DA6C5C 802B3CFB 22D8167F 4B52D6EB | 3165118C 135D81E4 6700B182 80A8D01D F39A4B1A 9C24748A EE3FC320 62DD251E | 697E02D5 0185F96C 420015F1 C03A2DD4 64593E0A BD0493E0 99D8774B 26C30C2F
40+ | ML-DSA-65 | 464756A9 85E5DF03 739D95DD 309C1ED9 C5B04254 CC294E7E 7EB9B936 5EE15117 | AE95EA0D AA80199E 7B4A74EB 5A1B1DC6 C3805BD0 1D2FA78D 7C4FBA8C 255AA13D | 491101BB A044DE6E 44A63796 C33CDA05 1BB05A60 725B87AF 4BA9DB94 0C03AC09 | 8E08EA0C 8DB94168 5B9905A7 3B0B57BA D3500B1F 73490480 B24375B4 1230CC04
41+ | ML-DSA-65 | 235A48DB 4CA7916B 884F424A 8586EFD5 17E87C64 AECEC0FC E9A3CC21 2BA1522E | 1AC58A90 9DB4D7BC 2473AB5E 24AF7682 79C76F86 A82D4482 58E24EEA 4EA6B713 | F8CE85CB 2EC474FF BF5A3FFA E029CE6F 4526B8D5 97655067 F97F438B 81071E9B | AE9531A0 1738615B 6D33C77B 3FF618A8 6E101FDC 4C850468 1F0EDFA6 4511AD63
42+ | ML-DSA-65 | E13131B7 05A76030 5FEFFEBF E99082E2 691A444B BEFCC3ED F67D9098 86200207 | B422093F 95CC489C 52F4FA2B 8973A2FD DD44426D 1D04D1AA EEFC8715 D417181F | CD365512 C7E61BBA A130800B 37F3BB46 AAF1BEEF 3742EA8A 9010A6DD 4576ED0B | 3C55E604 DECA7B89 A99305D7 A391C35F 66A17C19 23F46767 5EC951C0 948D21C9
43+ | ML-DSA-65 | 0A4793E0 40A4BC0D 0F37643D 12C1EA1F 10648724 609936C7 6E0EC83E 37209E92 | 622D26D5 36D4D66C D94956B3 3A74E2E8 30ED265D 25C34FF7 C3E52434 03146ADF | 6D9C7A79 5E48D80A 892CBF4D 45584297 87277E38 06EB5D0B CE1640EE BBBF9AEC | 3B141110 B9F56540 B2D49AAC DE639997 4A4EAC40 621E367E 68D4504F 294DB21B
44+ | ML-DSA-65 | F865B889 E5022D54 BABC81CA 67E7EB39 F1AC42F9 2CF5295C 3DA5C966 7DB1B924 | 45BC8EDD 1A620C46 E973E346 84427072 1824D978 88BC1742 81852D98 B7E8F4A3 | 047AFAAD BE020ED2 D766DA85 317DEDE8 0BE55054 5F0B21E3 F555A990 F8004258 | 56308A35 78360C41 356BA9C9 7D3240E0 1767FA76 BBBA9FD0 CC6CFA9A DD088DB9
45+ | ML-DSA-87 | 0D582191 32746BE0 77DFE821 E9F8FD87 857B28AB 91D6A567 E312A73E 2636032C | 4D261270 341A7AC6 B66900DD C2B8AB34 AB483C89 7410DDF3 B2C072BD DA416434 | 3AA49EF7 2D010AEC 19383BA1 E83EC2DD 3DCC207A 96FFCEB9 FFA269E3 E3D66400 | 5049DC39 045618B9 03C71595 B3A3E07A 731F95D3 7304623A CC98BCEF 4258B4CA
46+ | ML-DSA-87 | 146C47AB 9F88408E B76A8132 94D533B2 9D7E0FDA 75DA5A4E 7C69EB61 EFEEBB78 | 05194438 AF855B79 DB8CCCCB 647D6BA5 C7AAF901 BBD09D3B 29395F0E A431D164 | 82C44F99 8A8D24F0 56084D0E 80ECFD84 34493385 A284C699 74923C27 0D397782 | CFFC5988 A351E14A 3EE1282F 042A1436 79C45038 14296B27 993949A7 FF966F57
47+ | ML-DSA-87 | 049D9B0B 646A2AC7 F50B63CE 5E4BFE44 C9B87634 F4FF6C14 C513E388 B8A1F808 | AC8FE6B2 FE26591B 129EA536 A9A001C7 85D8ACBD D9489F6E 51469A15 6E9E635D | FEBC9F8A E159002B E1A11D39 5959DD7F C2071813 5690CDAA 2BCFB580 1C02AB89 | FF400608 9BDF7337 E868F86D DF48F239 D2A52EA1 D0F686E0 103BF19C 3B571DB1
48+ | ML-DSA-87 | 9823DDDE 446A8EA8 83DAD3AC 6477F798 39FDC2D2 DEF2416B E0A8B71C FBC3F5C6 | 525010E3 07C4EA76 67D54EE2 7007C219 B01F4CF8 8DC3AB2D E8E9AAA5 9440A884 | F7592C97 C1A96A2F 4053588F 5CDAD4C5 0BF7C375 2709854F A27779B4 45DD2BA2 | FD775760 2B83B0A6 7A314CD5 BCC880E7 AE47ACDF 4D6AF982 69028EFB 486838F7
49+ | ML-DSA-87 | AE213FE8 589B414F 53780D8B 9B683717 9967E13C B474C5AD 365C0437 78D2BC90 | D4988E91 064E5DF6 D867434D 1DED16DC D8533E39 E420DC2B 4EB9E40A 84146F7D | 19C1913B A76FF045 96BB7CC8 0FD825A5 AEDEF5D5 AD61CEDB 5203E6D7 EDB18877 | 23FE743E DD101970 D499E7EB 57A7AA24 5BAF417E 851B260C 55DD525A 445F08DA
5050|===
5151
5252[[rejections_table]]
5353.ML-DSA Algorithm 7 `ML-DSA.Sign_internal()` Known Answer Tests for Number of Rejection Cases
5454|===
5555| Security Level | Rejection Count | Seed | Key Hash | M' | Signature Hash
5656
57- | ML-DSA-44 | 77 | 090D97C1 F4166EB3 2CA67C5F B564ACBE 0735DB4A F4B8DB3A 7C2CE740 2357CA44 | 26D79E40 68040E99 6BC9EB50 34C20489 C0AD38DC 2FEC1918 D0760C86 21872408 | E3838364 B37F47ED FCA2B577 B20B80C3 CB51B9F5 6E0E4CDB 7DF002C8 74039252 | CD91150C 610FF02D E1DD7049 C309EFE8 00CE5C1B C2E5A32D 752AB62C 5BF5E16F
57+ | ML-DSA-44 | 77 | 090D97C1 F4166EB3 2CA67C5F B564ACBE 0735DB4A F4B8DB3A 7C2CE740 2357CA44 | 26D79E40 68040E99 6BC9EB50 34C20489 C0AD38DC 2FEC1918 D0760C86 21872408 | E3838364 B37F47ED FCA2B577 B20B80C3 CB51B9F5 6E0E4CDB 7DF002C8 74039252 | CD91150C 610FF02D E1DD7049 C309EFE8 00CE5C1B C2E5A32D 752AB62C 5BF5E16F
5858| ML-DSA-44 | 100 | CFC73D07 A883543A 804F7700 70861825 143A62F2 F97D05FC E00FD8B2 5D29A43F | 89142AB2 6D6EB6C0 1FA3F189 A9C87759 7740D685 983F29BB DD359664 8266AE0E | 0960C13E 9BA467A9 38450120 CC96FF6F 04B7E557 C99A8386 19A48F9A 38738AB8 | B6296FFF 0C1F23DE 4906D581 44B00A2D B13AD25E 49B4B857 3A62EFEE CB544DD7
59- | ML-DSA-65 | 111 | 111BDFD1 3CF30B4A 05F8C56E 91E20025 B284EFDC 661C349D 430FB988 149219EE | C06FE457 14696FF2 C77BB4CD 96E70BE9 539117AC 3D2E3F77 C736B060 8D9E78B6 | A30975C7 C58ABC8F E7FAE442 FE20F964 410B74E9 B4C1D47E 440223C5 A46DA72C | CADA29AE EC8E59CD 70747C2E 4C83F963 7E3C2495 3F11ADEE F586F786 35B3E60A
60- | ML-DSA-65 | 96 | F3A3F2C3 263A7042 95E9D9F7 3CD97D02 F4682BEE 5949C416 BC42C85B 7C864446 | 997CEE99 5EECE252 8155E1AE 0095116C 6D97B150 8B76AD25 BAE4ADF6 B60AE6A2 | 1C00F3E4 CF07BD4F B797D683 76EEC537 01730C49 09EC404F C93A6B7F 597F81B5 | 006B205B FA8DFF6C 2AA4237A 6BB5A33D BD1B3D97 13B99A9D 5AF9A882 CD0BA1E0
61- | ML-DSA-87 | 66 | C4B614E8 3CF6E25A 159A542B 9E132AA0 68FACCD8 755AA8B4 E22C6F6C 0438BF16 | 5BCAD035 7C6F3911 68B00523 CD7B1333 5F95996B F5432545 5484B830 15925580 | B9CFA245 C90359EF 041163A4 7231885E 56CB0215 984DE8A8 9941FE44 3CACEB61 | 5B23E5CE C5B09134 2EF7D5BB 8C50285A 9666CF93 7BBE1758 532B341B 0942994B
62- | ML-DSA-87 | 77 | 771E9543 4E410291 93D076B8 06F2C3C2 2A7F2060 287791E7 0F105ECA EAB7AD69 | C56A924B F6B046DA 3CACC10B 72749ECF 54266B38 A7E3D5C5 81D0A44F 1F3995D8 | C367382D 0E3FEE86 D29BAB0E E5FD6AE9 1B3A5A70 17A024CF 145A25F5 6A62B0B1 | 4996F774 3E90DAEB 61B5FF86 A868C9E5 195F201C 4E5F5A75 F4C79031 AAA6C544
59+ | ML-DSA-65 | 64 | 26B605C7 8AC762FA 1634C6F9 1DD117C4 FBFF7F3A 7E7781F0 CC83B628 1F04AD7F | 5DA13E57 1DF80867 A8F27E0F F81BE725 2A1ABF89 B3D6A03D 4036AF64 3EFBB04B | C9B07E7D DC027446 8F312F5C 692A54AC 73D1E34D 8638E20A 2CD3C788 F27D4355 | 12A4637E 3A833A5A 2A46F6A9 91399E54 4B62A230 B7AA82F7 366840FF 6A88DE61
60+ | ML-DSA-65 | 73 | 9191CF38 1BEE1747 5C011986 EFB6AFB1 EFA69974 42FD3342 7353F1DA 1AA39FC0 | 7930D4E5 2BA03B61 DAA57743 B39E291D 824DC156 356C6B1A 8232574D 5C8BDD08 | E616E36E 81AA1EC3 92621094 21AE0DDD A5E3B5A8 F4A252BC A27AE882 538DF618 | 3D758ACE 312433D7 80403B3D 4273171F B93D008B 39535214 2C6DC517 3E517310
61+ | ML-DSA-65 | 66 | 516912C7 B90A3DBE 009B7478 DBCAF0F5 C5C9ED96 99A20D0C A56CC516 E5A444CD | 0FD15951 B93A4D19 446B48D4 7D32D2CA 2253FF43 BB8CCCB3 4C07E5F1 A3181B7A | 9247CA75 F9456226 A0C783DA BCC33FF5 B4B48957 5ADED543 E74B29B4 5F9C8EF2 | E5CE2678 00EDF335 88451050 F9B4A5BF 97030D04 5132A7E3 ED9210E7 4028D23B
62+ | ML-DSA-65 | 65 | D4B841F8 82D50AB9 E590066B AFABA0F0 D04D3264 1C0B978E 54CCAA69 A6E8D2C4 | 0039C128 DDE6923E A08FF14F 5C5C66DC B282B471 FD1917DB EBE07C8C 45B73F8A | 17523165 7B0F3C70 65947999 467C3420 64F29BFA EB553E97 561407D5 560E3AEB | 8830EA25 4AF2854B F67C2B90 7E2321C9 4FD6EFB2 FDAA7766 9FC3A5C4 426C57C9
63+ | ML-DSA-65 | 64 | 5492EB8D 811072C0 30A30CC6 6B23A173 059EBA0D 4868CCB9 2FBE2510 B4A5915F | 573DCD99 C86DAE81 F6F80CB0 0AF40846 028EA8F9 FE63102F E4A78238 BC7B660E | 33D2753E D87D0003 B44C1AF5 F72EB931 F559C6B4 931AF7E2 49F65D3F A7613295 | 84D4AF50 933D6E13 D4332B86 AF0692A6 6F5030AB 01C2EAC4 131A5EEB F78CE9E5
64+ | ML-DSA-87 | 64 | B5C07ECE FE9E7C3B 885FDEF0 32BDF9F8 07B4011E 2DFE6806 C088D208 1631C8EB | 5D22F4C4 0F6EEB96 BB891DB1 5884ED4B 0009EA02 A24D9D1E 9ADFC81C 7A42EA7F | D1D5C2D1 67D6E629 06790A5F EDF5A0A7 54CFAF47 E6A11AEB 93FB8C41 934C31F8 | 54F0A9CB 26F98B39 4A35918E CA6760EB D10753FC 5CDBA8BE 508873AD 83538131
65+ | ML-DSA-87 | 65 | E8FC3C9F AD711DDA 2946334F BBD33146 8D6E9AB4 8EB86DCD 03F300A1 7AEBC5E5 | B6C4DC9B 20CE5D0F 445931EE 316CF067 6E806D1A 6A988688 81D060EA 27CEB139 | 3B435F7A 2CE431C7 AB8EAE09 91C5DAC6 10827C99 D2780304 6FBC6C56 7D6B71F2 | E337495F 08773F14 FB26A3E2 29B9B26D 086644C7 FDC30026 7F9DCDD5 D78DB849
66+ | ML-DSA-87 | 64 | 151F8088 6D6CE8C3 B428964F E02C40CA 0C8EFFA1 00EE089E 54D78534 4FCCF719 | 127972C3 3323FEFB F6B69C19 E0C86F41 558D9AB2 B1A8AD6F 39BD0A02 45DC8D7E | C628CE94 D2AA99AA 50CF15B1 47D4F9A9 C62A3D46 12152DE0 A502C377 F472D614 | 99B552B2 14325442 48BFF47A C8F24CB7 8DBB25C9 683F3ADC B75614BE D58A0358
67+ | ML-DSA-87 | 64 | 48BEFFB4 C97E59E4 74E1906F 39888BE5 AE62F6A0 11C05EF6 A6B8D1E5 4F2171B7 | 72DA77CF 563CBB53 0129F601 29AF989C A4036BA1 058267BF BA34A2C7 0BE803C4 | D2756A8F B4E47F79 6AF704ED 0FC8C6E5 73D42DFA B443B329 F00F8DB2 FF12C465 | E643914B 8556D053 60C65EB3 E7A06BE7 C398B82D 49973EEF DC711E65 B11EB5E8
68+ | ML-DSA-87 | 69 | FE2DA9DD 93A077FC B6452AC8 8D0A5762 EB896BAA AC6CE7D0 1CB1370B A8322390 | 7422DBE3 F476FFE4 1A4EFB33 F3DDFD8B 328029BA 30506038 66C36CFB C2EE4B87 | A86B29AD F2300D26 36E21D4A 350CD18E 55A25437 9C3659A7 A95D8734 CEC1F005 | 8D25818D D972FFF5 B9E9B4CC 534A9510 0A1340C1 C81D1486 A68939D3 40E0A58B
6369|===
6470
6571==== ML-DSA SigVer Test Types
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